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Inverse Trigonometric Functions

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  1. 1.Let =3 ^-1((6)/(11)) and =3 ^-1((4)/(9)), where inverse trigonometric functions take only …
  2. 2.If ( ^-1(x√2))= ( ^-1√1-x^2),x (0,1), then the value of x is:
  3. 3.Let 0< <1, =(1)/(3 ) and ^-1(1- )+ ^-1(1- )=( )/(4).
  4. 4.Considering the principal values of inverse trigonometric functions, the value of the expr…
  5. 5.If the domain of the function f(x)= ^-1(1x^2-2x-2), is (-, ] [ , ] [ ,), then + + + is equ…
  6. 6.The number of solutions of ^-14x+ ^-16x=( )/(6), where -12√6<x<12√6, is equal to :
  7. 7.If the domain of the function f(x)= ^-1((2x-5)/(11-3x))+ ^-1(2x^2-3x+1) is the interval [ …
  8. 8.The value of ^-1(√1+ ^2(2)-1 (2))- ^-1(√1+ ^2((1)/(2))+1 ((1)/(2))) is equal to
  9. 9.The sum of the infinite series ^-1((7)/(4))+ ^-1((19)/(4))+ ^-1((39)/(4))+ ^-1((67)/(4))+.
  10. 10.Considering the principal values of the inverse trigonometric functions, ^-1(√32 x+(1)/(2)…
  11. 11.Let [x] denote the greatest integer less than or equal to x.
  12. 12.( ^-1(3)/(5)+ ^-1(5)/(13)+ ^-1(33)/(65)) is equal to:
  13. 13.If > > >0, then the expression ^-1 +(1+ ^2)( - )+ ^-1 +(1+ ^2)( - )+ ^-1 +(1+ ^2)( - ) is …
  14. 14.If ( )/(2) x (3 )/(4), then ^-1((12)/(13) x+(5)/(13) x) is equal to
  15. 15.Using the principal values of the inverse trigonometric functions, the sum of the maximum …
  16. 16.Given that the inverse trigonometric function assumes principal values only.
  17. 17.If the domain of the function ^-1((3x-22)/(2x-19))+ _e(3x^2-8x+5x^2-3x-10) is ( , ], then …
  18. 18.If [a= ^-1( (5))] and [b= ^-1( (5))], then a^2+b^2 is equal to
  19. 19.For , , 0, if ^-1 + ^-1 + ^-1 = and ( + + )( - + )=3 , then equals
  20. 20.Let [x=(m)/(n)] (m, n are co-prime natural numbers) be a solution of the equation [ (2 ^-1…
  21. 21.Considering only the principal values of inverse trigonometric functions, the number of po…
  22. 22.If the domain of the function f(x)= _e(4x^2+11x+6)+ ^-1(4x+3)+ ^-1((10x+6)/(3)) is ( , ], …
  23. 23.Let (a, b) (0,2 ) be the largest interval for which ^-1( )- ^-1( )>0, (0,2 ), holds.
  24. 24.Considering the principal values of the inverse trigonometric functions, the sum of all th…
  25. 25.[ ^ - 1( ( - 5)) + ^ - 1( (6)) - ^ - 1( (12))] is equal to :(The inverse trigonometric fun…
  26. 26.If ( )/(4)+ _p=1^11 ^-1(2^p-11+2^2p-1)= , then is equal to ____ .
  27. 27.If k= (( )/(4)+(1)/(2) ^-1((2)/(3)))+ ((1)/(2) ^-1((2)/(3))), then the number of solutions…
  28. 28.Let the maximum value of ( ^-1x)^2+( ^-1x)^2 for x [-√32,1√2] be (m)/(n) ^2, where gcd(m,n…
  29. 29.y= (( )/(3)+ ^-1(x)/(2))(x-y)^2+3y^2 Answer: 3
  30. 30.Let S = x: ^-1x= + ^-1x+ ^-1[2x+1].
  31. 31.If for some , ; , + =8 and ^2( ^-1 )+ ^2( ^-1 )=36, then ^2+ is __________ Answer: 14
  32. 32.Let the inverse trigonometric functions take principal values.
  33. 33.For n N, if ^-13+ ^-14+ ^-15+ ^-1n=( )/(4), then n is equal to ________.
  34. 34.For [x (-1,1]], the number of solutions of the equation [ ^-1 x=2 ^-1 x] is equal to _____…
  35. 35.If S=x R: ^-1(x+1x^2+2x+2)- ^-1(xx^2+1)=( )/(4), then _x s( ((x^2+x+5)( )/(2))- ((x^2+x+5)…
  36. 36.If the domain of the function f(x)= ^-1((2x)/(5x+3)) is [ , )U( , ], then |3 +10( + )+21 |…
  37. 37.Let a_1=1,a_2,a_3,a_4, ..
  38. 38.If k=(4+12^-123)+(12^-123), then the number of solutions of the equation ^-1(kx-1)=^-1x-^-…
  39. 39.Let =3^-1(611) and =3^-1(49), where inverse trigonometric functions take only the principa…
  40. 40.If, for some , with and +=8, ^2(^-1)+cosec^2(^-1)=36, then ^2+ is ____.
  41. 41.If y=(3+^-1x2), then (x-y)^2+3y^2 is equal to _______.
  42. 42.If >>>0, then ^-1+1+^2-+^-1+1+^2-+^-1+1+^2- is equal to :
  43. 43.(^-135+^-1513+^-13365) is equal to:
  44. 44.Considering the principal values of the inverse trigonometric functions, ^-1(√32x+12√1-x^2…
  45. 45.The sum of the infinite series ^-1(74)+^-1(194)+^-1(394)+^-1(674)+ is :
  46. 46.The value of ^-1(√1+^2 2-1 2) - ^-1(√1+^212+112) is equal to
  47. 47.Considering only the principal values of inverse trigonometric functions, the number of po…
  48. 48.Let x=m/n (m,n are co-prime natural numbers) be a solution of the equation (2^-1x)=19 and …
  49. 49.^-1(1+√33+√3)+^-1(8+4√36+3√3) is equal to
  50. 50.If the sum of all the solutions of ^-1(2x1-x^2)+^-1(1-x^22x)=3, -1<x<1, x0, is -4√3, then …